6 papers
On one class of nowhere non-monotonic functions with fractal properties that contains a subclass of singular functions
S. O. Klymchuk, M. V. Pratsiovytyi
We study one class of continuous functions defined on segment by equality $$ f(x)=δ_{α_1(x)1}+\sum^{\infty}_{k=2}\left[δ_{α_k(x)k}\prod^{k-1}_{j=1}g_{α_j (x)j}\rig…
Frequency of a Digit in the Representation of a Number and the Asymptotic Mean Value of the Digits
S. O. Klymchuk, O. P. Makarchuk, M. V. Pratsiovytyi
We study the relationship between the frequency of a ternary digit in a number and the asymptotic mean value of the digits. The conditions for the existence of the asymptotic mean…
Transformations and functions that preserve the asymptotic mean of digits in the ternary representation of a number
M. V. Pratsiovytyi, S. O. Klymchuk, O. P. Makarchuk
In the paper we study transformations of the interval and functions that preserve the asymptotic mean of the digits in the --adic representation of a number , $$r…
Topological, metric and fractal properties of the set of real numbers with a given asymptotic mean of digits in their -adic representation in the case when the digit frequencies exist
M. V. Pratsiovytyi, S. O. Klymchuk
In the paper we describe some properties of function of -a…
Linear fractals of the Besicovitch-Eggleston type
M. V. Pratsiovytyi, S. O. Klymchuk
We study topological, metric and fractal properties of set of numbers with given asymptotic mean of digits in their ternary representation. We investigate connection of the…
Asymptotic mean of digits of the -representation of the fractional part of a real number and related problems of fractal geometry and fractal analysis
M. V. Pratsiovytyi, S. O. Klymchuk
We introduce a concept of asymptotic mean of digits (symbols) in the -representation of a real number, that is a generalization of the -adic representation and have a self-…